Existence and synthesis of complex hopfield type associative memories

Garimella Rama Murthy, Moncef Gabbouj

    Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

    2 Citations (Scopus)


    In this research paper, a complex valued generalization of associative memory synthesized by Hopfield is considered and it is proved that it is impossible to synthesize such a neural network with desired unitary stable states when the dimension of the network (number of neurons) is odd. The linear algebraic structure of such a neural network is discussed. Using Sylvester construction of Hadamard matrix of suitable dimension, an algorithm to synthesize such a complex Hopfield neural network is discussed. Also, it is discussed how to synthesize real/complex valued associative memories with desired energy landscape (i.e. desired stable states and desired energy values of associated quadratic energy function).

    Original languageEnglish
    Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    PublisherSpringer Verlag
    Number of pages14
    ISBN (Print)9783319192215
    Publication statusPublished - 2015
    Publication typeA4 Article in conference proceedings
    EventInternational Work Conference on Artificial Neural Networks -
    Duration: 1 Jan 1900 → …

    Publication series

    NameLecture Notes in Computer Science
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349


    ConferenceInternational Work Conference on Artificial Neural Networks
    Period1/01/00 → …

    Publication forum classification

    • Publication forum level 1

    ASJC Scopus subject areas

    • General Computer Science
    • Theoretical Computer Science


    Dive into the research topics of 'Existence and synthesis of complex hopfield type associative memories'. Together they form a unique fingerprint.

    Cite this